Asymptotic normality through factorial cumulants and partitions identities
Konstancja Bobecka-Wesołowska , Pawel Hitczenko , Fernando Lopez-Blazquez , Grzegorz Rempala , Jacek Wesołowski
AbstractIn the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments, as (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for "moments" of partitions of numbers. The general limiting result is then used to (re)derive asymptotic normality for several models including classical discrete distributions, occupancy problems in some generalized allocation schemes and two models related to negative multinomial distribution.
|Journal series||arXiv:1106.4684, (0 pkt)|
|Keywords in English||Mathematics - Probability, Primary 60F05, Secondary 05A17, 11P84|
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